Problem: Michael is 40 years younger than Ashley. Ashley and Michael first met 3 years ago. Five years ago, Ashley was 5 times older than Michael. How old is Ashley now?
Explanation: We can use the given information to write down two equations that describe the ages of Ashley and Michael. Let Ashley's current age be $a$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $a = m + 40$ Five years ago, Ashley was $a - 5$ years old, and Michael was $m - 5$ years old. The information in the second sentence can be expressed in the following equation: $a - 5 = 5(m - 5)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to solve our first equation for $m$ and substitute it into our second equation. Solving our first equation for $m$ , we get: $m = a - 40$ . Substituting this into our second equation, we get the equation: $a - 5 = 5($ $(a - 40)$ $ -$ $ 5)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $a - 5 = 5a - 225$ Solving for $a$ , we get: $4 a = 220$ $a = 55$.